J . Am. Chem. SOC.1982, 104, 5604-5607
5604
:Room Temp.
0 :Low Temp.
Acknowledgment. This work was supported by the U S . Public Health Service (GM-19450), the U S . Army Research Office (DAAG29-82-K-0024), and the Danish Natural Science Research Council. Technical assistance of Ludmila Jonas is gratefully acknowledged.
088 -
0,7-
Kz
0.60.5 -
010
through additional work, but the data base presented here can serve as a useful set of test cases against which more detailed models of orientation can be evaluated.
0,I
0.2
0,3
0,4
0.5
Figure 9. Orientation factors of selected hydrocarbons at room and at low temperatures (see text).
has not been possible from the observed spectra. The main advantage of the method is its extreme simplicity, which now makes the determination of absolute polarization directions of electronic and vibrational transitions in most aromatic molecules a trivial task. The main shortcoming of the method is its purely empirical nature. The detailed mechanism of the orientation effect of stretched polyethylene can only be established
Registry No. 1, 28820-47-5; 2, 92-94-4; 3, 135-48-8; 4, 15254-25-8; 5, 213-46-7; 6, 613-06-9; 7, 782-23-0; 8, 92-24-0; 9, 189-55-9; 10, 52518-8; 11, 886-66-8; 12, 207-08-9; 13, 224-41-9; 14, 23913-06-6; 15, 193-43-1; 16, 198-55-0; 17, 120-12-7; 18, 13214-70-5; 19, 501-65-5; 20, 624-38-4; 21, 581-40-8; 22, 86-73-7; 23, 132-65-0; 24, 207-11-4; 25, 92-82-0; 26, 1012-72-2; 27, 206-44-0; 28, 529-85-1; 29, 259-79-0; 30, 117-80-6; 31, 203-12-3; 32, 215-58-7; 33, 484-1 1-7; 34, 6333-43-3; 35, 230-17-1; 36, 132-64-9; 37, 260-94-6; 38, 86-74-8; 39, 85-01-8; 40, 106-37-6;41, 2379-55-7; 42, 195-19-7; 43, 24300-95-6; 44, 523-27-3; 45, 1564-64-3; 46, 781-92-0; 47, 779-02-2; 48, 10103-06-7;49, 191-24-2; 50, 129-00-0; 51, 771-97-1; 52, 4145-24-8; 53, 150-78-7; 54, 779-03-3; 55, 605-48-1; 56, 3674-69-9; 57, 95-94-3; 58, 1079-71-6; 59, 781-43-1; 60, 24300-91-2; 61, 28172-99-8; 62, 208-20-8; 63, 193-85-1; 64, 3141-27-3; 65, 81626-25-7;66, 191-68-4; 67, 191-07-1;68,253-52-1; 69, 13638-84-1; 70, 274-09-9; 71, 3002-81-1; 72, 91-20-3; 73, 217-59-4; 74, 95-50-1; 75, 83-32-9; 76, 5325-97-3; 77, 625-84-3; 78, 638-02-8; 79, 612-71-5; 80, 16458-17-6; 81, 87-85-4; 82, 891-22-5; 83, 6830-78-0; 84, 20343-16-2; 85, 82823-46-9; 86, 340-99-8; 87, 17597-70-5; 88, 54100-60-6; 89, 20672-23-5; 90, 27884-38-4;91, 82823-47-0;92, 209-42-7; 93,6580-41-2; 94, 23062-31-9; 95,934-36-1; 96,2164-87-6; 97, 27884-37-3; 98,403937-6; 99, 15881-33-1; 100, 82823-48-1; 101, 13019-33-5; 102, 210-80-0; 103, 194-00-3; 104, 40237-01-2; 105, 21 1-53-0; 106, 181-82-8; 107, 275-51-4; 108, 32495-80-0; 109, 930-35-8; 110, 27884-36-2; 111, 20896-8; 112, 50356-52-0; polyethylene, 9002-88-4.
Temperature Dependence of Excimer Formation between Pyrenes at the Ends of a Polymer in a Good Solvent. Cyclization Dynamics of Polymers. 8? A. E. C. Redpath and M. A. Winnik* Contribution from the Lash Miller Laboratories, Department of Chemistry, and Erindale College, University of Toronto, Toronto, Ontario, Canada M5S 1 A l . Received February 4, 1982
Abstract: The kinetics of intramolecular pyrene excimer formation have been studied in dilute toluene solution as a function of temperature for polystyrene molecules capped on both ends with pyrene groups. Three samples, of M , 3900, 6600, and 9200, were examined. The cyclization rate constant ( k , ) was sensitive to chain length and had an E, of 3.4 kcal/mol. Excimer dissociation back to locally excited pyrene (k-,) was insensitiue to chain length and had an E, = 10.4 kcal/mol. Hence for these polymers, the AHo for pyrene excimer formation is 7 kcal/mol, very similar to that of pyrene itself.
Since the initial report in 1965 by Hirayama,' numerous reports have appeared describing intramolecular excimer formation in bichromophoric molecules and intramolecular exciplex formation between different groups at the ends of short-chain molecules.* These phenomena are of interest for a variety of reasons. With these molecules one can explore how the stereochemical constraints of the chain affect excimer and exciplex spectroscopy. In other instances, these kinds of molecules permit one to study interactions between pairs of chromophores a t high dilution. Our interest is in the shape and motion of polymer chains. When one studies intramolecular cyclization between groups at the ends of long
Scheme I
'This paper is dedicated to Mr. Schuster of the Centre de Recherches sur les Macromoltcules in Strasbourg, France, on the occasion of his retirement.
polymer chains, one can in principle obtain information about chain conformation and chain dynamics. These inferences depend
0002-7863/82/ 1504-5604$01.25/0
0 1982 American Chemical Society
J . Am. Chem. Sot., Vol. 104, No. 21, 1982 5605
Cyclization Dynamics of Polymers upon the validity of the mechanism one invokes to describe the reaction kinetics as well as the depth of one’s knowledge of the spectroscopy of end-group interaction for intramolecular excimer or exciplex formation. By analogy with bimolecular excimer kinetic^,^ one normally invokes the mechanism in Scheme I to describe intramolecular excimer and exciplex formation. This “two-state” mechanism, involving one locally excited state 1* and one excimer state 2*, represents the simplest possible scheme to account for the possible reversibility of excimer formation. It assumes implicitly that the correlation function of the chain-end displacement in 1* decays as a single exponential that can be described by a single rate constant (kl). We have presented in Scheme I the particular case of intramolecular pyrene [Py] excimer formation first studied by Zachariasse4 and later extended to polymer chains by Cuniberti and Perico5 and by ourselves.6 The rate constant k l describes the diffusion-controlled excimer forming process and k-, its dissociation to the ring-opened form with a locally excited pyrene. The rate constants kM (kM = km + k n M ) and kE (kE = kw + knE) describe the sums of radiative and nonradiative decays of the pyrene and pyrene excimer, respectively. For a given chain length at sufficiently low temperature, the process described by k-, becomes so slow that one can neglect it. As in all diffusion-controlled processes, kl is a function of time. Its dependence upon time depends upon the distribution of endto-end distances in 1* and how this distribution function evolves in time. In this sense, the time dependence of kl resembles that of the second-order rate constant for diffusion-controlled bimolecular reactions in solution. These points were first considered in the now classic papers of Wilemski and Fixman (WF)’ and elaborated upon by Dois and by Perico and C ~ n i b e r t i . The ~ essential feature of these arguements is that Scheme I in its simplest form suffices to describe (the long time) cyclization dynamics only if a single mean relaxation time for the chain serves as the rate-limiting step for cyclization. Otherwise, one must consider explicitly the distribution of configurations of 1* at t = 0 and the time dependence of k , . For chains of 3 , 4 , or 5 atoms, the numbers of discrete configurations of 1 are small, and there are frequently several distinct pathways of comparable rate to interconvert 1* to l’*. Recent results from DeSchryver’s laboratoryl0 and Eisenthal’s group” support this point of view. This paper presents studies on pyrene-substituted polymers of the form Py-polystyrene-Py, 1, for chains of 60-200 bonds. We lCH~l~C02CH~CH2-ICHCH~l,~CH~CHl~-CH~CH~O~C~CH~l~
I
Ph
Ph
1.x “ Y
@
show for polymers of sufficiently narrow molecular weight distribution that Scheme I is adequate to describe cyclization. We (1) (a) Hirayama, F. J . Chem. Phys. 1965, 42, 3163. (b) Chandross, E. A.; Dempster, C. J. J . A m . Chem. Soc. 1970, 92, 3586. (2) DeSchryver, F. C.; Boens, N.; Put, J. Adu. Photochem. 1977, 10, 359. (3) (a) Hui, M. H.; Ware, W. R. J . A m . Chem. Soc. 1976, 98,4722. (b) Stevens, B.; Ban, M. .I.Trans. Faraday Soc. 1964,60, 1515. (c) Forster, T.; Kasper, K. Z . Phys. Chem. (Wiesbaden) 1954,1,275; 2.Electrochem. 1955, 59, 976. (d) Birks, .I. B. ‘Photophysics of Aromatic Molecules”; Wiley: New York, 1970. (4) Zachariasse, K. A.; Kiihnle, W. Z . Phys. Chem. (Wiesbaden) 1976, 101, 267. (5) Cuniberti, C.; Perico, A. Eur. Polymn. J . 1977,13, 369; 1980, 16,887. ( 6 ) (a) Redpath, A. E. C.; Winnik, M. A. Ann. N.Y. Acad. Sci. 1981, 366, 75. (b) Winnik, M. A,; Redpath, A. E. C.; Richards, D. H. Macromolecules 1980, 13, 328. (7) Wilemski, G.; Fixman, M. J . Chem. Phys. 1974, 60, 866, 878. (8) Doi, M. Chem. Phys. 1975, 9, 455. (9) Perico, A.; Cuniberti, C. J . Polym. Sci., Polym. Phys. Ed. 1977, 15, 1435. (10) Van der Auweraer, M.; Gilbert, A.; DeSchryver, F. C. J . Am. Chem. SOC.1980, 102, 4007. (11) Wang, Y.; Crawford, M. K.; Eisenthal, K. B. J . Phys. Chem. 1980, 84, 2696-2698.
Py-POLYSTYRENE-Py in t o l u e n e
20 -
0 360
400
440
480
520
560
600
WAVELENGTH [nm]
Figure 1. Fluorescence spectra of Py-PS3900-Py at 19 “C and at 50 O C , normalized a t the (0,O) band of the pyrene fluorescence.
find that k-, and kE are independent of chain length, whereas k l is very sensitive to chain length, and that the activation energies associated with kl and k-, are entirely consistent with cyclization being a diffusion- (encountered-) controlled process leading to a tightly bound pyrene excimer. We find that the binding energy (AHo)for intramolecular excimer formation in 1 is very similar to that of the excimer formed bimolecularly from two pyrenes. Experimental Section The polymer samples were prepared as described previously.6,’2 Solutions of 2 X IO” M in purified toluene were degassed and sealed into Pyrex tubes under a vacuum better than torr. Fluorescence decay times were measured by the time-correlated single-photon counting technique. Pyrene fluorescence decays fM(t) were measured at 380 nm. Pyrene excimer fluorescence decays were measured in the wavelength interval 515-550 nm. Steady-state emission spectra were run on an SLM Model 4000 fluorimeter and were not corrected. Fluorescence spectra of one of the polymer samples at two different temperatures are presented in Figure 1.
Results and Discussion Viability of Scheme I. Scheme I predicts that the blue pyrene fluorescence in 1 should decay as a sum of two exponential components, with decay constants A, and A,. Under the same conditions, the excimer emission IE(t) should grow in and decay as the difference of two exponential terms (a3 = -a4) with the same decay constants. I M ( t ) = al exp(-A,t) a, exp(-A,t) (1) I E ( t ) = a3 exp(-A,t) a4 exp(-A,?) (2)
+ +
The AI,, values are related to the rate constants in Scheme I by the expression A,, A, = ‘/Z((X + Y) 7 [ ( Y- 4 2 + 4 k , k - , ] l q (3) a2
A, - x
a,
x - A,
-=-
(4)
To obtain rate constants from the decay data, one needs not only values for AI,, and a2/a1but also an independent measure of kM. A convenient way of solving this problem is to assume that the decay constant dA,, of an appropriate model compound containing a single pyrene provides a measure of kM. We chose as our model a polystyrene sample of &fn= 5900 containing a pyrene at only one end. We assume for each temperature that kM = Am&. A simplification occurs if 4klk-, is much smaller than ( Y - X),. The I M ( t )decays become exponential with a decay constant A, = X = k , + kM. The A2 values obtained from the rise time of the excimer equal Y = k-l + kE. Note that when k , is relatively small, this result might obtain even if k-, is comparable in value to kE. We have found that at 22 O C in toluene, I M ( t ) decays can be fit to a single exponential, with x 2 values close to 1.1, over two and a half decades of the emission decay for each of the three (12) Redpath, A. E. C.; Winnik, M. A., to be published.
5606 J. Am. Chem. SOC.,Vol. 104, No. 21, 1982
Redpath and Winnik
Table I. Decay Times and Rate Constants for Py-polystyrene Samples in Toluene at 71 "C
M, 3900
1.08
Na 80
6600
1.12
9200
1.13
Z,IM,,
10-7k1),
io-v.,,
S-
S-
10-7kE, s-
( ~ ~ ~ ;9' , n s
1.37
3.35
2.35
0.41
135
0.74
2.95
1.85
0.25
185
0.50
3.07
1.86
0.16
~ ~ - 1 ,
x2
104 112 131 136 143 150
1.23 1.20 1.23 2.09 0.97 1.33
ns
15.0 18.2 18.7 11.8 18.9
15.1 a Mean chain length, calculated
from [@,
- 450)/52] + 15 =n(bonds).
9 00
5 0"
25"
I
I
dn
Py-polystyrene- Py
a,la,;a,la,
-0.93 0.204 -0.94 0.134 -0.91 0.086
(K,) = k,)/k.,.
0 3900 8 6600
in toluene
0
9200
I
I
I
I
2.7
2.9
3.1
3.3
1000/ T
22 to I u ene
1
lXlO6
2.7
OK-'
Figure 2. Arrhenius plot of log ( k , )vs. l/Tfor Py-polystyrene-Py: (0) Py-PS3900-Py; (m) Py-PS6600-Py; ( 0 ) Py-PS9200-Py.
polystyrene samples. For the emission decay to the exponential, W F theory requires a corresponding exponential decay for the mean correlation function p ( t ) = (G(r,t)G(r,t+ 7 ) ) of the chain end displacement. Consequently, end-to-end cyclization is dominated by a single mode of the chain motion, which we assign to T , , the slowest internal relaxation time of the chain. At temperatures above 30 OC, the decay of IM(t) is no longer exponential. If these deviations from exponentially have their origin in the growing importance of the k-l process at elevated temperatures, the I M ( t ) and I E ( t )data should satisfy both eq 1 and 2. This is found to be the case. X1 and X2 values from the two experiments are similar; -a3/u4values are essentially unity; and the x2 for the data are acceptable. The data in Table I are typical. They have been chosen to emphasize that there are differences in the values from the two experiments, with the poorest result for all our experiments shown for X2 (fin= 6600). X1 values from zM(t) decays are consistently 4-8% larger than those from IE(t)decays, and a3/u4is always in the range -0.93 to -0.97. These deviations may arise from the finite dispersity of chain lengths in our polymer samples and from the possible presence of 1% or less of polymers in our sample containing only one pyrene. We take the overall agreement as further support of the validity and applicability of Scheme I. Rate constants calculated from the data for the three Pypolystyrene-Py samples at 71 "C in toluene are also reported in Table I. From the table, it may be seen that k-, and kE values are not sensitive to chain length, whereas k , and K , (= k l / k - , , the equilibrium constant for end-to-end cyclization) decrease substantially with an increase in chain length. Results at other temperatures support these observations. Since kl and K 1are so sensitively dependent upon chain length, we emphasize by angle brackets, ( ) , in the discussion that follows that ( k , ) and ( K , ) , calculated from our data, describe values averaged over the small but finite polydispersity of molecular weights in each of our polymer samples.
3.1
2.9
1000/ T
3.3
3.:
O K - '
Figure 3. Arrhenius plots of log k-, vs. l/T: (0),Py-PS3900-Py; (m) Py-PS6600-Py; ( 0 )Py-PS9200-Py. TEMPERATURE
90" I
"t
50' I
25O
IOo
I
I
TOLUENE
7.0
L
7.0
\ \
3.0
\ \
\
I
\
\ \
\ I .o
\ I
I
I
L
Figure 4. Arrhenius plots of log k , (0)and log k M ( 0 )vs. 1 / T . The k~ data represent averaged values from the polymer samples at each temperature. Also shown is a portion of the best-fit straight line of the k-l plot from Figure 3.
Temperature Dependence of the Rate Constants. A plot of log ( k , ) vs. 1 / T is shown in Figure 2, log k-l vs. 1 / T in Figure 3, and plots of log kM and log k , vs. 1 / T in Figure 4. Good Arrhenius behavior is observed for each of the rate constants. The
J . Am. Chem. SOC.,Vol. 104, No. 21, 1982 5607
Cyclization Dynamics of Polymers
Table 111. Cyclization Probabilities and Entropies for Py-polystyrene-Py in Toluene Mn AScv, cal deg-' mol-' W(0)'"
Table 11. Activation Energies'" and Preexponential Factors for Excimer Formation in Py-polystyrene-Pyin Toluene k
A exp (-Ea/RT), s-'
@n
1.00 X l o 9 exp(-2.9/RT) 1.65 X l o 9 exp(--3.8/RT) 8.05 x lo8 exp(-3.5/RT) 1.17 x 1014 exp(-l0.4/RT) k-, 6.63 X lo' exp(-O.bO/RT) kEC 1.33 x IO7 exp(-0.41/RT) kM a E, in kcaymol. The average valueE,((k,)) for the three samples is 3.41 kcaymol. From the combined data for all three samples. (k,P
3900 6600 9200
activation energies for ( k , ) for each of the polymer samples are similar and probably identical within experimental error. The excimer dissociation process described by k-, is independent of chain length at all temperatures and is by far the process most sensitive to temperature. The temperature sensitivity of k-, is typical of tha,; of all tightly bound excimers and exciplexes of bimolecular origin.13 Note that kM and kEare relatively insensitive to temperature. Activation energies for these processes and their respective preexponential A factors are collected in Table 11. The binding energy of the excimer could be calculated from & ( ( k l ) ) - E,(k-,) = AHo by using the averaged values of the activation energies from the three polymer samples. The value of AHo = -7.0 kcal/mol is typical of pyrene excimers. For example, pyreiie itself in cyclohexane forms an excimer with = -8.0 k c a l / ~ n o l . ' ~ The activaf.ion energy E a ( ( k l ) )for the cyclization step, 3.4 kcal/mol, is of' particular interest in the area of polymer dynamics. Its meaning d8:pends upon the model one invokes to interpret this value. In the Rouse and Zimm models,'~~ the motion associated with ( k l ) is delocalized over the entire chain, with a node at the center of mac,s. The activation energy for ( k , ) should be that of a typical diffusion process, where Ediffcan be obtained from an Arrhenius plot of T/qo,where qo is the solvent viscosity. For example, Per ico and Cunibertig have argued that kl
= B(Dtr/RG2)
(5)
where D,, is the translational diffusion constant of the polymer, RG2is its mean-squared radius of gyration, and B is a proportionality constant whose value is model dependent. Since for polystyrene iii a good solvent RG2changes very little with temperature,I5 the Arrhenius behavior of k l must reflect that of Dt,. Edigfor toluene is 2.31 kcal/mol,I6 about 1 kcal/mol smaller than E a ( ( k l ) ) .We believe this difference to be outside of current experimental 'error, which suggests that certain details of the model above may ne:ed to be reconsidered. On the other hand, E,( ( kl )) is significantly smaller than the barrier for internal backbone rotation, estimated at greater than 5 kcal/mol for p01ystyrene.I~ Kramers's theory17J8provides a different basis for interpreting activation energies for dynamic processes in polymers. Under the conditions of high viscous damping, E, can be written as the sum (13) Birks. .I.B. ReD. Prop. Phvs. 1975. 38. 903. (14) Birks; .I.B.; Limb, M. D.;Munro, I. H'. Proc. R. SOC.London, Ser. A 1964. 280. 289. (lS)'Akcasu, A. Z . ; Han, C. C . Macromolecules 1979, 12, 216. (16) (a) Ritldick, J. A.; Bunger, W. B. "Organic Solvents", 3rd Ed.; Wiley-Interscienci:: New York, 1970. E,,, is calculated from d In (vo/T)/d(1/7'). E, is calculated from d In qo/d(l/T). (b) Birks found E, for pyrene bimolecular ex:imer formation to be 3.0 kcal/mol in t01uene.l~
(17) Friedrich, C.; LauprZte, F.; Nod, C.; Monnerie, L. Macromolecules
1981, 14, 11 19. ( 1 8 ) Kramers, H.
A. Physica. (Amsterdam) 1940, 7, 284.
-21.gb 1.61 x 10-5 -23.1b 9.18 X 10.' -24.0b 5.56 X 10.' '" From W ( 0 ) = exp(ASCy/R). A S values were obtained from (K,) values at each temperature, using AH = -7.0 kcal/mol, and aver aged. 3900 6600 9200
of the activation energy for the solvent viscosity (E,) and the height of the internal potential barrier (E*).
Ea((k~)= ) E,
+ E*((ki))
(6)
Since the value of E, for toluene is 2.08 kcal/mol,I6 this identifies end-to-end cyclization with a process with an internal potential barrier of 1.3 kcal/mol. Chain Conformation and Dynamics. According to W F t h e ~ r y , ~ k , N-312 for a polymer in a 0 solvent, where the distribution function of the end-to-end displacement is Gaussian in form and N is the chain length. In good solvents, where the chains are N-915 in the limit of long chain length. These swollen, k , predictions follow also from eq 5 : in a 0 solvent, D N-'/2,RG2 N, whereas in a good solvent, RG2 flywith v = 3/5, and in the limit of long chain length, D N-".I9 Our previous experiments, in toluene at 22 OC and in cyclohexane at 34.5 OC, the 0 temperature, have been in accord with these observations. One issue of current concern in polymer science is whether dynamic processes of polymers scale according to the same critical exponents as thermodynamic p r ~ p e r t i e s . ' ~This J ~ matter is less controversial in 0 solvents than in good solvents where excluded volume considerations become important. Our results permit us to comment on one aspect of this problem. From Table 1 and Figure 3, we find that k q is not sensitive to chain length. Since the equilibrium constant ( K , ) for end-to-end cyclization is equal to ( k , ) / k - , ,we conclude that ( k , ) and ( K , ) must show identical dependencies on chain length. This confirms an observation first made for cyclohexane solutions of Py-polystyrene-Py at the 0 temperature.20 Our data provide one other piece of information relevant to the can study of chain conformation. The entropy of cyclization SCy be calculated for each chain length, and from these values, we can estimate the cyclization probabilities W(0): W(0) = e a d R
-
-
-
--
-
These values are collected in Table 111. W(0) varies from 1.6 X for the polymer of mean chain length N = 80 bonds to W(0) = 5.6 X for the sample with = 185 bonds. These results emphasize how sensitive cyclization probability is to the length of the chain separating the chromophores on the chain ends.
m
Acknowledgment. We thank NSERC Canada and the donors of the Petroleum Research Fund, administered by the American Chemical Society, for their support of this research. We acknowledge the help and support of Dr. K. Zachariasse (Gottingen), through the auspices of a NATO grant, for making us aware of certain experimental difficulties and for his valuable suggestions. (19) Experimental values of Y for dynamic measurements (D,,, intrinsic viscosity) of polymers are smaller than the assymptotic value predicted from theory and of values of Y determined from radius of gyration measurements. See, for example: Han, C. C. Polymer 1979, 20, 1083. Weill, G.; desCloizeaux, J. J . Phys. Lett. (Orsay, Fr.) 1979, 40, 99. (20) Redpath, A. E. C.; Winnik, M . A. J . Am. Chem. SOC.1980, 102, 6443.
